The figure below is made up of a rectangle and two identical squares. AB is twice the length of BQ. What is the length of PQ if AB is 14 cm long.

1. Break Down the Problem

The problem involves a rectangle and two identical squares. We need to determine the length of $PQ$. Given that $AB$ is twice the length of $BQ$ and $AB = 14$ cm, we can express $BQ$ in terms of $AB$.

2. Relevant Concepts

In this case:

• Let $BQ = x$.
• Therefore, since $AB$ is twice $BQ$, we have: $AB = 2 \cdot BQ = 2x$
• Given $AB = 14$ cm, we can set up the equation: $2x = 14$

3. Analysis and Detail

Now we will solve for $x$:

1. Divide both sides of the equation by 2: $x = \frac{14}{2} = 7 \text{ cm}$
2. So, $BQ = 7$ cm.

4. Verify and Summarize

Now that we have $BQ = 7$ cm, $PQ$ is equal to $BQ$ since both squares are identical and the side lengths of the squares are equal to $BQ$.

Final Answer

Thus, the length of $PQ$ is $7$ cm.